Percentiles for unequal probability sample

On Nov 20, 2013, at 11:35 AM, Trevor Walker wrote:

I often work with tree data that is sampled with probability proportional
to size, which presents a special challenge when describing the frequency
distribution.  For example, R functions like quantile() and fitdistr()
expect each observation to have equal sample probability.  As a workaround,
I have been "exploding"/"mushrooming" my data based on the appropriate
expansion factors.  However, this can take a LONG TIME and I am reaching
out for more efficient suggestions, particularly for the quantile()
function.  Example of my workaround:

The 'Hmisc' package has a `wtd.quantile` function. I seem to remember that it might have been borrowed from the quantreg package.

# trees.df represents random sample with probability proportional to size
(of diameter) using "basal area factor" of 20
trees.df <- data.frame(Diameter=rnorm(10, mean=10, sd=2),
TreesPerAcre=numeric(10))
trees.df$TreesPerAcre <- 20/(trees.df$Diameter^2*pi/576)    # expansion
factor for each observation

# to obtain percentiles that are weighted by trees per acre, "explode"
diameter data
explodeFactor <- 10 # represents ten acres
treeCount <- sum(round(trees.df$TreesPerAcre*explodeFactor ))
explodedDiameters.df <- data.frame(Diameter=numeric(treeCount))
k=0 # initialize counter k
for (i in 1:length(trees.df$Diameter)){
for (j in 1:round(trees.df$TreesPerAcre[i]*explodeFactor)){
  k <- k +1
  explodedDiameters.df$Diameter[k] <- trees.df$Diameter[i]
 }
}

quantile(explodedDiameters.df$Diameter) # appropriate percentiles (for
trees per acre)
quantile(trees.df$Diameter)             # percentiles biased upwards



Trevor Walker

-- 

David Winsemius
Alameda, CA, USA